+- MKLab (https://mklab.gr)
+-- Forum: [INDEX] (https://mklab.gr/forumdisplay.php?fid=1)
+--- Forum: SCIENTIFIC COMPUTING (https://mklab.gr/forumdisplay.php?fid=4)
+---- Forum: COMPUTATIONAL MATHS (https://mklab.gr/forumdisplay.php?fid=68)
+----- Forum: BOOKS (https://mklab.gr/forumdisplay.php?fid=69)
+----- Thread: Numerical Linear Algebra and Optimization [Gill] (/showthread.php?tid=2119)
Numerical Linear Algebra and Optimization [Gill] - mklabgr - 09-23-2026
Numerical Linear Algebra and Optimization by Philip E. Gill, Walter Murray, and Margaret H. Wright is a comprehensive treatment of two closely connected areas of computational mathematics: numerical linear algebra and linear optimization. The book develops practical algorithms for solving linear systems, including Ax=bAx=b, compatible and singular systems, and linear least-squares problems, while emphasizing the realities of finite-precision computation.
A major theme is the relationship between mathematical conditioning, numerical stability, and the efficiency of algorithms. The authors use a concrete, computational approach to linear algebra, including matrix factorizations and techniques such as updating LU factorizations.
The second half moves from linear algebra toward optimization, introducing linear programming and then developing the simplex method in detail. The book explains why linear programming is important across economics, operations research, algorithm analysis, combinatorics, cryptography, and computational science, and connects optimization theory with numerical computation.
Originally developed from a classic 1991 text and republished by SIAM in 2021, the 426-page volume is intended both as a reference and as a textbook, with numerous exercises; SIAM specifically notes that Chapters 6–8 can support an upper-division course on linear least squares and linear programming.
BOOK